conspire/constitutive/solid/hyperelastic/gent/
mod.rs

1#[cfg(test)]
2mod test;
3
4use crate::{
5    constitutive::{
6        ConstitutiveError,
7        solid::{Solid, TWO_THIRDS, elastic::Elastic, hyperelastic::Hyperelastic},
8    },
9    math::{IDENTITY, Quantity, Rank2, TensorRank4},
10    mechanics::{CauchyStress, CauchyTangentStiffness, Deformation, DeformationGradient, Scalar},
11    units::{EnergyDensity, Stress},
12};
13
14#[doc = include_str!("doc.md")]
15#[derive(Clone, Debug)]
16pub struct Gent {
17    /// The bulk modulus $`\kappa`$.
18    pub bulk_modulus: Quantity<Stress>,
19    /// The shear modulus $`\mu`$.
20    pub shear_modulus: Quantity<Stress>,
21    /// The extensibility $`J_m`$.
22    pub extensibility: Scalar,
23}
24
25impl Gent {
26    /// Returns the extensibility.
27    pub fn extensibility(&self) -> Scalar {
28        self.extensibility
29    }
30}
31
32impl Solid for Gent {
33    fn bulk_modulus(&self) -> Quantity<Stress> {
34        self.bulk_modulus
35    }
36    fn shear_modulus(&self) -> Quantity<Stress> {
37        self.shear_modulus
38    }
39}
40
41impl Elastic for Gent {
42    #[doc = include_str!("cauchy_stress.md")]
43    fn cauchy_stress(
44        &self,
45        deformation_gradient: &DeformationGradient,
46    ) -> Result<CauchyStress, ConstitutiveError> {
47        let jacobian = self.jacobian(deformation_gradient)?;
48        let isochoric_left_cauchy_green_deformation =
49            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
50        let (
51            deviatoric_isochoric_left_cauchy_green_deformation,
52            isochoric_left_cauchy_green_deformation_trace,
53        ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
54        let denominator =
55            self.extensibility() - isochoric_left_cauchy_green_deformation_trace + 3.0;
56        if denominator <= 0.0 {
57            Err(ConstitutiveError::custom(
58                "Maximum extensibility reached.",
59                self,
60            ))
61        } else {
62            Ok((deviatoric_isochoric_left_cauchy_green_deformation
63                * self.shear_modulus()
64                * self.extensibility()
65                / jacobian)
66                / denominator
67                + IDENTITY * self.bulk_modulus() * 0.5 * (jacobian - 1.0 / jacobian))
68        }
69    }
70    #[doc = include_str!("cauchy_tangent_stiffness.md")]
71    fn cauchy_tangent_stiffness(
72        &self,
73        deformation_gradient: &DeformationGradient,
74    ) -> Result<CauchyTangentStiffness, ConstitutiveError> {
75        let jacobian = self.jacobian(deformation_gradient)?;
76        let inverse_transpose_deformation_gradient = deformation_gradient.inverse_transpose();
77        let isochoric_left_cauchy_green_deformation =
78            deformation_gradient.left_cauchy_green() / jacobian.powf(TWO_THIRDS);
79        let (
80            deviatoric_isochoric_left_cauchy_green_deformation,
81            isochoric_left_cauchy_green_deformation_trace,
82        ) = isochoric_left_cauchy_green_deformation.deviatoric_and_trace();
83        let denominator =
84            self.extensibility() - isochoric_left_cauchy_green_deformation_trace + 3.0;
85        if denominator <= 0.0 {
86            Err(ConstitutiveError::custom(
87                "Maximum extensibility reached.",
88                self,
89            ))
90        } else {
91            let prefactor = self.shear_modulus() * self.extensibility() / jacobian / denominator;
92            Ok((TensorRank4::dyad_ik_jl(&IDENTITY, deformation_gradient)
93                + TensorRank4::dyad_il_jk(deformation_gradient, &IDENTITY)
94                - TensorRank4::dyad_ij_kl(&IDENTITY, deformation_gradient) * (TWO_THIRDS)
95                + TensorRank4::dyad_ij_kl(
96                    &deviatoric_isochoric_left_cauchy_green_deformation,
97                    deformation_gradient,
98                ) * (2.0 / denominator))
99                * (prefactor / jacobian.powf(TWO_THIRDS))
100                + TensorRank4::dyad_ij_kl(
101                    &(IDENTITY * (0.5 * self.bulk_modulus() * (jacobian + 1.0 / jacobian))
102                        - deviatoric_isochoric_left_cauchy_green_deformation
103                            * prefactor
104                            * ((5.0
105                                + 2.0 * isochoric_left_cauchy_green_deformation_trace
106                                    / denominator)
107                                / 3.0)),
108                    &inverse_transpose_deformation_gradient,
109                ))
110        }
111    }
112}
113
114impl Hyperelastic for Gent {
115    #[doc = include_str!("helmholtz_free_energy_density.md")]
116    fn helmholtz_free_energy_density(
117        &self,
118        deformation_gradient: &DeformationGradient,
119    ) -> Result<Quantity<EnergyDensity>, ConstitutiveError> {
120        let jacobian = self.jacobian(deformation_gradient)?;
121        let factor = (deformation_gradient.left_cauchy_green().trace() / jacobian.powf(TWO_THIRDS)
122            - 3.0)
123            / self.extensibility();
124        if factor >= 1.0 {
125            Err(ConstitutiveError::custom(
126                "Maximum extensibility reached.",
127                self,
128            ))
129        } else {
130            Ok(0.5
131                * (-self.shear_modulus() * self.extensibility() * (1.0 - factor).ln()
132                    + self.bulk_modulus() * (0.5 * (jacobian.powi(2) - 1.0) - jacobian.ln())))
133        }
134    }
135}
conspire/constitutive/solid/hyperelastic/gent/mod.rs

conspire/constitutive/solid/hyperelastic/gent/
mod.rs
